10. Zhalnin R.V., Masyagin V.F., Peskova E.E., et al. Modeling the Flow of Multicomponent Reactive Gas on Unstructured Grids

UDK 519.63:533.6.011.72

DOI: 10.15507/2658-4123.030.202001.162-175

Modeling the Flow of Multicomponent Reactive Gas on Unstructured Grids

Ruslan V. Zhalnin
Leading Researcher, Head of Chair of Applied Mathematics, Differential Equations and Theoretical Mechanics of Faculty of Mathematics and Information Technology, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), Associate Professor, ResearcherID: Q-6945-2016, ORCID: https://orcid.org/0000-0002-1103-3321, This email address is being protected from spambots. You need JavaScript enabled to view it.

Victor F. Masyagin
Senior Researcher, Associate Professor of Chair of Applied Mathematics, Differential Equations and Theoretical Mechanics of Faculty of Mathematics and Information Technology, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ResearcherID: C-2439-2013, ORCID: https://orcid.org/0000-0001-6738-8183, This email address is being protected from spambots. You need JavaScript enabled to view it.

Elizaveta E. Peskova
Researcher, Associate Professor of Chair of Applied Mathematics, Differential Equations and Theoretical Mechanics of Faculty of Mathematics and Information Technology, National Research Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Ph.D. (Physics and Mathematics), ResearcherID: U-7971-2019, ORCID: https://orcid.org/0000-0003-2618-1674, This email address is being protected from spambots. You need JavaScript enabled to view it.

Vladimir F. Tishkin
Head of Department of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences (4 Miusskaya Sq., Moscow 125047, Russia), D.Sc. (Physics and Mathematics), Professor, Corresponding Member of RAS, ResearcherID: R-5820-2016, ORCID: https://orcid.org/0000-0001-7295-7002, This email address is being protected from spambots. You need JavaScript enabled to view it.

Introduction. The article deals with mathematical modeling of the subsonic flow of a multicomponent reactive mixture in a flowing chemical reactor. The numerical algorithm is based on the finite volume method; the calculation is performed on unstructured triangular grids using the Message Passing Interface parallel computing technology.
Materials and Methods. To describe the flows under studying, the Navier–Stokes equations are used in the approximation for low Mach numbers. To solve these equations, the finite volume method on unstructured triangular grids is used. The study uses a splitting scheme for physical processes, namely, the chemical kinetics equations responsible for the transformations of substances are first solved, and then the equations describing the conservation laws of momentum and energy for each component of the gas mixture are solved. To find numerical flows through the edges of the grid elements, the Lax–Friedrichs–Rusanov scheme is used. To solve the equations of chemical kinetics, a compact algorithm proposed by the team led by N.N. Kalitkin is used. The METIS library is used to divide the grid into connected subdomains with an approximately equal number of cells. To organize parallel computing, Message Passing Interface technology is used.
Results. The article presents a numerical algorithm for studying multicomponent gas flows on unstructured triangular grids taking into account viscosity, diffusion, thermal conductivity, and chemical reactions. As a result of the study, a numerical simulation of the flow of a subsonic multicomponent gas in a flowing chemical reactor was carried out using ethane pyrolysis as an example. Computational, known numerical solutions and experimental data of ethane pyrolysis in a flowing reactor are compared.
Discussion and Conclusion. The numerical results on the conversion of the initial gas mixture are in good agreement with the known experimental data. The presented distribution patterns of the main components of the mixture and gas-dynamic parameters correspond to the flow pattern observed experimentally. Further work in this direction involves the modeling of subsonic gas flows on unstructured tetrahedral meshes using algorithms of higher accuracy for a more accurate study of ongoing processes.

Keywords: Navier–Stokes equations, subsonic flows, low Mach number, chemical kinetics, ethane pyrolysis, unstructured triangular grids

Funding: The work was supported by the Ministry of Science and Higher Education of the Russian Federation (No. 1.6958.2017/8.9), the Russian Foundation for Basic Research (Project No. 18-31-00102) and a grant of the President of the Russian Federation for young Russian scientists (MK-2007.2018.1).

For citation: Zhalnin R.V., Masyagin V.F., Peskova E.E., et al. Modeling the Flow of Multicomponent Reactive Gas on Unstructured Grids. Inzhenernyye tekhnologii i sistemy = Engineering Technologies and Systems. 2020; 30(1):162-175. DOI: https://doi.org/10.15507/2658-4123.030.202001.162-175

Contribution of the authors: R. V. Zhalnin – research methodology development; V. F. Masyagin – implementation of the algorithm and the software complex; E. E. Peskova – search for the calculation algorithm, study of the numerical results; V. F. Tishkin – problem formulation and general work management.

All authors have read and approved the final manuscript.

Received 13.09.2019; revised 07.11.2019; published online 31.03.2020

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